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Munich Personal RePEc Archive

The effects of background music and sound in economic decision making:

Evidence from a laboratory experiment

Fujikawa, Takemi and Kobayashi, Yohei

Graduate School of Business, Universiti Sains Malaysia, Advanced Medical and Dental Institute,Universiti Sains Malaysia

6 April 2010

Online at https://mpra.ub.uni-muenchen.de/23374/

MPRA Paper No. 23374, posted 23 Jun 2010 06:35 UTC

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The effects of background music and sound in economic decision making: Evidence from a

laboratory experiment

Takemi Fujikawa

Yohei Kobayashi

June 14, 2010

Abstract

This paper experimentally studies the effects of background music and sound on the pref- erence of the decision makers for rewards in pairwise intertemporal choice tasks and lot- tery choice tasks. The participants took part in the current experiment, involving four treat- ments: (1) the familiar music treatment; (2) the unfamiliar music treatment; (3) the noise treatment and (4) the no music treatment. The experimental results confirm that background noise affects human performance in decision making under risk and intertemporal decision making, though the results do not indicate the significantfamiliarityeffect that is a change of the preference in the presence of familiar back- ground music and sound.

Keywords: Allais-type preferences; choice un- der risk; intertemporal choice; the familiarity effect

1 Introduction

This paper shall experimentally investigate the relation between the background mu- sic/sound and behavioural preference (i.e., risk and time preference). For investigat- ing risk preference, this paper elicits decision- making preferences in “choice under risk”, that is, choices under the followings: (1) low- and high-money payoffs (e.g., a choice be- tween a 80% chance of winning 400 yen and

Graduate School of Business, Universiti Sains Malaysia. Email:takemi@usm.my.

Advanced Medical and Dental Institute, Universiti Sains Malaysia. Email:kobapie@gmail.com.

sure 300 yen; a choice between a 80% chance of winning 4000 yen and sure 3000 yen) and;

(2) low- and high-probability payoffs (e.g., a choice between a 80% chance of winning 4000 yen and sure 3000 yen; a choice between a 20% chance of winning 4000 yen and a 25%

chance of winning 3000 yen). On the other hand, for investigating time preference, this paper elicits decision-making preferences in intertemporal choice, that is, choices under the followings: (1) smaller-sooner and smaller- later money payoffs (e.g., a choice between 800 yen in 7 days and 880 yen in 30 days;

a choice between 700 yen in 7 days and 770 yen in 30 days); (2) larger-sooner and larger- later money payoffs (e.g., a choice between present 5000 yen and 5500 yen in 30 days; a choice between present 5000 yen and 5005 yen in 7 days) and; (3) smaller-sooner and larger- longer money payoffs (e.g., a choice between 800 yen in 7 days and 1600 yen in 14 days; a choice between 900 yen in 7 days and 1800 in 14 days).

The goal of the present study is to see if fa- miliar and unfamiliar background music and the white noise sound could affect the be- haviour of the participants, who were asked to make decisions in choice under risk and in- tertemporal choices. The current experiment was conducted to examine the effects of the background music and sound presented to the participants during their choice tasks, involv- ing choice under uncertainty and intertempo- ral choice. We used three forms of background music and sound (i.e., familiar music, unfamil- iar music and noise). We shall show an exten- sive analysis that was made to answer central questions:

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• Do familiar and unfamiliar background music and the white noise sound affect human behaviour? Do people change their behaviour in the presence of these background music and sound?

• Do people behave exhibiting the increased or attenuatedfamiliarity effectin the pres- ence of familiar background music? Does familiar background music facilitate or detract the familiarity effect when people engage in decision making?

The organisation of this paper is as follows:

Section 2 provides a sketchy description of choice under risk and intertemporal choice.

Section3is devoted to review literature on ef- fects of background music in decision making.

In Section 4, we discuss details of the current experiment. Section 5contains a general dis- cussion of the experimental results. Finally, we conclude.

2 Decision Making under Risk and with Intertempo- ral Choice

Economists have been analysing, both theoret- ically and experimentally, “choice under risk”

and “intertemporal choice”, as the analysis has much to contribute to the study of economics onrationality. As we shall show below, this pa- per aims to investigate behavioural tendencies when people engage in decision making un- der risk and decision making with intertempo- ral choice in the presence of particular back- ground music and sound. Our aim is worth- while, as there should be much discussion on the effect of background music and sound in our daily decision making (e.g., consumer be- haviour).

On the one hand, much attention has been focused on choice under risk and its related

“Allais-type” behaviour (Allais, 1953) to ex- emplify deviations from rationality. Since Allais (1953), there have been a number of experiment-based studies, investigating and demonstrating human behaviour in decision making under risk. One of the most elegant studies isKahneman and Tversky(1979). They performed a choice experiment, where they asked the participants to choose between: (H1)

a 80% chance to win $4 and (L1) a sure gain of $3. The results revealed that many of the participants preferred a safe option (L1). This preference for a certain payoff is termed as the certainty effect. In another experiment,Kahne- man and Tversky(1979) asked the participants to choose between (H2) a 20% chance to win $4 and (L2) a 25% chance to win $3. Many of the participants preferred (H2). This participants’

response is well known asAllais paradox.

On the other hand, preferences in intertem- poral consumption choice under certainty were in previous studies (e.g. Green, Fristoe and Myerson, 1994; Kirby and Herrenstein, 1995;Millar and Navarick,1984;Solnick, Kan- nenberg, Eckerman and Waller, 1980). Fred- erick and Loewenstein (2002) introduced an example, where people make choice between:

(H3) a sure gain of $101 in 101 days and (L3) a sure gain of $100 in 100 days. Many would pre- fer (H3). By decreasing day length, this choice problem could be reduced to the choice prob- lem between: (H4) a sure gain of $101 tomor- row and (L4) a sure gain of $100 today. Many people would prefer (L4), though it has a lower objective value. This behavioural tendency is consistent with the existing body of literature (McKerchar, Green, Myerson, Pickford, Hill and Stout,2009) which supports the assertion that people often choose an option that yields sooner reward even if it has a lower reward when they make a choice between two rewards that differ in delay. Furthermore, Takahashi (2009) demonstrated that subjects often prefer small-sooner rewards to larger-later rewards.

The aforementioned preference reversal phenomena raise an issue relevant to economic theory. It has been examined and reported in the tradition of Samuelson’s (Samuelson, 1937) model of discounted utility that ex- plains patterns of intertemporal choice, and Von Neumann-Morganstern expected utility theory (von Neumann and Morgenstern,1944) that is a rational choice model in economics.

Despite these elegant models, recent and pre- vious studies have provided robust evidence for a number of “anomalies” and “violations”

in intertemporal choice and decision making under risk. Frederick and Loewenstein(2002) provide historical origins of the discounted utility model and a convincing discussion on the model. We note here that the results and findings are inconsistent, despite many lab-

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oratory experiments conducted by researchers across countries.

3 Effects of Background Mu- sic in Decision Making

Music is a most specialised, peculiar hu- man cultural artefact (Andrade, 2004; Bea- ment,2001) and powerful stimulus to our be- haviour and decision making. One raises a question: Can background music affect our be- haviour? There has been much of the con- troversy pertaining to this question (Brayfield and Crockett,1955;Jacob,1968;McGehee and Gardner, 1949; Milliman, 1982; Smith, 1947;

Uhrbrock, 1961). Hilliard and Tolin (1979) showed that performance in the presence of fa- miliar background music is higher than that in the presence of unfamiliar music. Corhan and Gounard (1976) premised that vigorous rock music should be associated with better performance than easy-listening music. Mu- sic is employed in the background of offices and retail stores to produce certain desired behaviours and decision making among em- ployees and/or customers (Milliman, 1982).

Bruner(1990) presumed that music affects hu- man beings in various ways as long as they play music. Having accepted this presump- tion, previous researchers presented study on behavioural effects on music in decision mak- ing.

There exists literature pertinent to the ef- fects of music on behaviour and decision mak- ing. Iwanaga and Ito(2002) examined the dis- turbance effect of music on human behaviour in memory tasks. They conducted an ex- periment in which the participants performed choice tasks in the presence of vocal music, instrumental music, a natural sound and no music. We here note that vocal music con- tains more verbal information than instrumen- tal music (Iwanaga and Ito, 2002). Iwanaga and Ito (2002) reported that highest distur- bance was observed under the vocal music condition. Sundstrom and Sundstrom (1986) showed that music was effective in maintain- ing both arousal and motivation when the de- cision makers (DMs) were performing easy decision-making tasks.Wolf and Weiner(1972) asked undergraduates to perform a mental arithmetic task with having them listen to rock

music, and showed that their performance in the task was neither decreased nor increased.

Hence, the effects of background music in de- cision making are inconsistent. The kinds of background music varied: classical (Hilliard and Tolin,1979), folk (Mowsesian and Heyer, 1973), hard rock (Wolf and Weiner,1972), vo- cal and instrumental (Salam´e and Baddeley, 1982), pop (Iwanaga and Ito, 2002). All of background music in these studies consisted of existing songs (e.g., Mozart, well-known Japanese pop songs, and so on).

3.1 The Familiarity Effect

It must be noted at the outset that, in previous experiments, the “familiarity effect” was likely to be idiosyncratic among individual partic- ipants. The familiarity effect is a change of preference in the presence of familiar back- ground music/sound. The previous authors conducted experiments in which the partici- pants were asked to perform the tasks in the presence of background music that was chosen

— either biasedly or unbiasedly — from the list ofexistingsongs (e.g., Mozart inRauscher, Shaw and Ky(1993)).

Thus, the previous experiments were con- ducted with the setting where the songs used as background music during the experiments had been accessible (i.e., purchasable and downloadable). This setting is inadequate since it leads to all sorts of difficulties with ex- perimental controls, in such a way that impres- sion towards particular songs was idiosyn- cratic among the participants. For example, some of the participants had or had not been familiar with the songs; they had or had not had prior personal images or preconceived opinions of the songs. If (some of) the partic- ipants had had prior personal images or pre- conceived opinions of the songs used as back- ground music during the experiment, it would more or less affect their behaviour. Lack of control with respect to how familiar the songs are may produce results that cannot be inter- preted clearly, as different participants may ac- tivate different mechanisms to the “same” mu- sical stimulus, with resulting differences in be- haviour (Juslin and V¨astfj¨all,2008). Thus, pre- vious results more or less were biased by the familiarity effect.

The familiarity effect is concerned with

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episodic memory that refers to a process whereby an emotion is induced in a listener, as the music evokes a memory of a partic- ular event in the listener’s life (Juslin and V¨astfj¨all,2008). Music often evokes memories (Gabrielsson,2001;Juslin, Laukka, Liljestr ¨om, V¨astfj¨all and Lundqvist, L.-O.,submitted;Slo- boda,1992), and the emotion is associated with the memories. Such a emotion can be rather intense (Juslin and V¨astfj¨all, 2008). Baum- gartner(1992) showed that episodic memories evoked by music tend to involve not only so- cial relationships (e.g., past or current roman- tic partners) but private relationships (e.g., the death of grandfather). Episodic memory can be one of the most frequent and subjectively important sources of emotion in music (Juslin and Liljestr ¨om,in press;Sloboda and O’Neill, 2001). Thus, the familiarity effect and its re- lated effect of the episodic memory cannot be neglected.

In the current experiment, the song was used which had not been available to the pub- lic before the experiment. The coauthor of the current paper, who is a composer of mu- sic, developed and composed the song used as background music for the current experi- ment that was neither downloadable norpur- chasable. Thus, the current experiment was carried out with the setting, where none of the participants had had an opportunity in listen- ing to and knowing the song before the ex- periment. This setting conforms to the behav- ior of the DMs, who have no personal images and/or preconceived opinions of the song.

4 Experiment

The current experiment was conducted at the Kyoto Experimental Economics Laboratory (KEEL) in Japan. On arrival at the KEEL, each participant was assigned a workstation that displayed an experimental screen, and distributed a written instruction that was read aloud. In the instructions, the participants were told that they could have a right to leave the laboratory before the experiment started, if they did not wish to participate in the ex- periment. The participants were also told that they were given an opportunity to ask ques- tions individually before and during the ex- periment. At the conclusion of the experiment,

they were paid individually and privately ac- cording to their response to choice problems, the detailed procedures of which shall be de- scribed below. The participants received no initial (showing up) fee. Decision task comple- tion took no longer 90 minutes, and an average payoff was 3735 yen (about 40 US dollars at the time of the experiment) per participant.

4.1 Participants

The participants in the current experiment were 42 undergraduates from various faculties at Kyoto Sangyo University, of whom were 6 women and 36 men. These participants had a mean age of 20.73 years (SD = 2.8, range= 18−34 years).

4.2 Apparatus

The experiment included four treatments:

• Treatment 1 in which the participants made decisions in the presence offamiliar background music;

• Treatment 2 in which the participants made decisions in the presence ofunfamil- iarbackground music;

• Treatment 3 in which the participants made decisions in the presence of noise (white noise);

• Treatment 4 in which the participants made decisions without the presence of any background music/sound.

The background music/sound was played in each treatment through personal head- phones that were connected with each work- station. As the order of the four treatments was randomised, each participant took part in the four treatments in a different order. For ex- ample, the order of the treatments performed by some participants was Treatment 2, 1, 3 and 4; while the order by the other participants was Treatment 3, 4, 1 and 2. She/he started with the first treatment and participated in the second treatment. On completion of the first treatment, she/he was advised by the automatically-generated message on the com- puter screen that the first treatment had been completed, and a 10-minutes break was given before starting the second treatment. During

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the 10-minutes break, she/he participated in a questionnaire shown on the computer screen and used a mouse to respond to a set of ques- tions. During the break, she/he was allowed to remove the headphone.

In each treatment, each participant was asked to respond to 30 random samples of pairwise choice problems taken by a computer programme from 120 choice problems, consist- ing of the following three types:

• Type A: Choice under risk (i.e., a choice between ap1chance of winningx1yen to- day and ap2chance of winningx2yen to- day (p1,p2∈(0, 1],p1x1>p2x2);

• Type B: Intertemporal choice (i.e., a choice between surey1yen int1days and surey2 yen int2days (y1 >y2 >0 andt1>t2≥ 0);

• Type C: Self-evident choice (i.e., a choice between aq1chance of winningz1yen to- day and aq2chance of winningz2yen to- day (q1,q2∈[0, 1),q1q2, 0<z1z2); a choice between surez3yen today and sure z4yen today (z3>z4>0))

Appendix 1 presents the payoff structure of the 120 choice problems, of which 60 are Type A problems; 40 are Type B problems and; 20 are Type C problems. Some choice problems shared the same payoff structure. For exam- ple, two Type A problems (Problem 2 and 8) involved a choice between 80% chance of winning 4000 yen and sure payoff of 3000 yen. Yet, the participants were presented with these problems in different paradigms:

Problem 2 was presented with a “probability- based” paradigm (that is shown in Figure 1), while Problem 8 with a “description-based”

paradigm (that is shown in Figure2).

That is, in each treatment, each participant was given 30 choice problems that were ran- domly selected for her/him by the computer programme from the pool of 120 choice prob- lems. The participants participated in all of the four treatments. The order of the treat- ments was, however, counterbalanced to avoid the “order effect” that is concerned with an indication that the order in which items are presented can affect the strength of the deci- sion maker’s belief (Zhang, Johnson and Wan, 1998).

Figure 1: Experimental screen for a probability-based paradigm. The upper of the display shows the choice problem.

The lower shows options available to the participants. They were asked to choose (click) either of the two options.

Figure 2: Experimental screen for a description-based paradigm.

In each treatment, the participants’ task was to make a selection between two options in the choice problem given at each roundt(t = 1, . . . , 30). As shown in Figure1 and 2, each of the problems was presented in their com- puter screen at each roundt. They were asked to respond to each problem by choosing (click- ing) one of two options (i.e., a left button and right button in the lower panel of Figure1and 2) by using a computer mouse. Each problem was the independent one-shot problem and ar- ranged randomly. The order of the problems and options was counterbalanced randomly across the participants.

On completion of each treatment — except for Treatment 4 —, the participants were asked

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to fill in a questionnaire developed to clar- ify the participants’ understanding on music preference, familiarity of the background mu- sic/sound played during the treatment and consciousness about the music/sound.

4.3 Treatment 1: A Familiar Music Treatment

4.3.1 Stimuli

The musical piece used in Treatment 1 as back- ground music was a popular song in Japan:

An opening song of Doraemon — famous TV Japanimation — that was arranged by the coauthor of the current paper, and used only for the experiment.1 In the treatment, only instrumental selections (e.g., piano) were em- ployed. Hence, as stated inMilliman(1982), no concern had to be given to female versus male vocalist, popular versus less popular artists, etc.

The song was arranged to piano solo score and performed by a virtual grand piano — the software synthesiser Ivory Grand Pianos stan- dardised by VSTi that emulates “Boseudofer 290 Imperial Grand”. No other particular ar- tificial instruments were used, except of other equipments for auditory correction (i.e., the equaliser, reverb and mastering effects). The music tempo was fixed as 120 beats per minute (bpm) and loop was arranged for continuous experiment. (Note that 1 loop is 1 minute.) The sound pressure of the 2 MIX source was nor- malised as -15 dB and its range is − dB to -0.1 dB (no clip). The format of sound source was 16 bits/44.1 kHz CD quality wave format without any compression. The average of note tone was C4; the highest note was G5 and; the lowest note was B2 (as chromatic scale). The density of notes was 250 notes per minute. Av- erage velocity of note was 100 (highest: 127, lowest: 64). The volume of the music was maintained at a constant level with the head- phones. The volume among each participant was all the same and fixed to proper loudness through the treatment continuously. Results of the questionnaires revealed that no partic- ipants expressed discomfort or distaste for the music played during the treatment.

1A succinct description ofDoraemon is found inIyer (2006).

4.3.2 Results

An overall proportion of risky choices (Prisky) was 0.5. The Prisky of individual participants is available in Appendix 2. Figure3 presents numbers of risky and safe choices of individ- ual participants in the treatment. We can see from the figure the existence of heterogene- ity among the participants in behavioural ten- dencies in the treatment. For example, Prisky of some participants (e.g., Participant 7) was 100 percent; while Prisky of other participants (e.g., Participant 1) was nearly 10 percent. Fig- ure 7 presents the distribution of the indi- vidual Prisky in the treatment (SD = 0.27).

The Prisky of individual 60 Type A problems is available in Appendix 4. Figure5 presents numbers of risky and safe choices of indi- vidual problems in the treatment. Figure 9 presents the distribution of Prisky of the indi- vidual problems (SD=0.23).

An overall proportion of sooner choices (Psooner) was 0.6. The Psooner of individual participants is available in Appendix 3. Fig- ure 4 presents numbers of sooner and later choices of individual participants in the treat- ment. We can see from the figure the exis- tence of heterogeneity among the participants in behavioural tendencies in the treatment. For example, some participants (e.g., Participant 36) chose only sooner options, while others (e.g., Participant 3) chose only later options.

Figure8presents the distribution of the indi- vidual Psooner in the treatment (SD = 0.32).

The Psooner of individual 40 Type B problems is available in Appendix 5. Figure6 presents numbers of sooner and later choices of indi- vidual problems in the treatment. Figure 10 presents the distribution ofPsooner of the indi- vidual problems (SD=0.26).

An overall proportion of rational choices made among Type C problems was 1. We posit in this paper that, given a choice between a q1 chance of winning z1 yen today and a q2 chance of winning z2 yen today (q1,q2 ∈ [0, 1),q1q2, 0 < z1 < z2), it is rational for people to choose aq1chance of winningz1yen today. We also posit that, given a choice be- tween surez3yen today and surez4yen today (z3>z4>0), it is rational for people to choose surez3yen today.

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Figure 3: Numbers of risky and safe choices of individual participants in Treatment 1. For example, Participant 20 was presented with 16 Type A choice problems, and chose risky options in 2 problems and safe options in 14 problems.

Figure 4: Numbers of sooner and later choices of individual participants in Treatment 1. For ex- ample, Participant 38 was presented with 13 Type B choice problems, and chose sooner options in all of the 13 problems.

Figure 5: Numbers of risky and safe choices in individual 60 Type A questions in Treatment 1.

For example, Problem 16 was performed by 12 participants, and 6 of them chose risky options and the rest 6 chose safe options.

Figure 6: Numbers of sooner and later choices in individual 40 Type B questions in Treatment 1. For example, Problem 77 was performed by 11 participants, and 10 of them chose sooner options and 1 chose later options.

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Figure 7: The distribution ofPriskyof the indi- vidual participants in Treatment 1. For exam- ple, we observed 6 out of 42 participants (i.e., Participant 4, 7, 8, 19, 23 and 39), whosePrisky was more than 0.9.

Figure 8: The distribution ofPsoonerof the indi- vidual participants in Treatment 1. For exam- ple, we observed 2 out of 42 participants (i.e., Participant 18 and 41), whose Psooner is such that 0.3<Psooner0.4.

4.3.3 Questionnaire Analysis

On completion of the treatment, the partic- ipants were asked to fill in a questionnaire developed to clarify the participants’ under- standing on music preference, familiarity of the background music played during the treat- ment and consciousness about the music. The questionnaire contained questions that were:

(1) Was the music played during this treatment familiar to you? (2) How much attention did you pay to the music during this treatment? (3) Do you like the music? (4) Do you think your decision-making behaviour was influenced by the music?

Results of the questionnaires revealed the followings: First, self-reported familiarity level of the music on a 11-point scale (0=not famil- iar with; 10=very much familiar with) was ex-

Figure 9: The distribution ofPrisky of the indi- vidual Type A problems in Treatment 1. For ex- ample, 1 out of 60 Type A problems (i.e., Prob- lem 6) was observed, where 0.8<Prisky0.9.

Figure 10: The distribution of Psooner of the individual Type B problems in Treatment 1.

For example, 1 out of 40 Type B problems (i.e., Problem 61) was observed, where 0.1 <

Psooner0.2.

tremely high (Min = 9,Max = 10,M = 9.90,SD = 0.37). Second, self-reported atten- tion level (i.e., how much attention paid to the music while making decisions) on a 11-point scale (0=no attention at all; 10=very much atten- tion) was high (Min = 0,Max = 10,M = 7.47,SD = 2.97). Third, self-reported music liking on a 11-point scale (0=dislike very much;

10=like very much) was high (Min = 0,Max = 10,M = 7.76,SD = 2.56). Fourth, self- reported influence of the music on decision- making behaviour (i.e., to what extent the par- ticipants’ decision-making behaviour was in- fluenced by the music) on a 11-point scale (0=to no extent; 10=to a very large extent) was low (Min=0,Max=10,M=3.00,SD=3.14).

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Figure 11: Numbers of risky and safe choices of individual 42 participants in Treatment 2. For example, Participant 19 was presented with 18 Type A choice problems, and chose only risky options in all of the 18 problems.

Figure 12: Numbers of sooner and later choices of individual 42 participants in Treatment 2. For example, Participant 12 was presented with 11 Type B choice problems, and chose only sooner options in all of the 11 problems.

Figure 13: Numbers of risky and safe choices in individual 60 Type A problems in Treatment 2.

For example, Problem 24 was performed by 16 participants, and 8 of them chose risky options and the rest 8 chose safe options.

Figure 14: Numbers of sooner and later choices of individual 40 Type B problems in Treatment 2. For example, Problem 95 was performed by 10 participants, and all of them chose only sooner options.

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Figure 15: The distribution of Prisky of the in- dividual participants in Treatment 2. For ex- ample, we observed 2 out of 42 participants, whosePriskywas less than 0.1.

Figure 16: The distribution ofPsoonerof the in- dividual participants in Treatment 2. For ex- ample, we observed 8 out of 42 participants were observed, whose Psooner was more than 0.9.

4.4 Treatment 2: An Unfamiliar Mu- sic Treatment

4.4.1 Stimuli

The musical piece used in Treatment 2 as back- ground music was a new song composed and arranged by the coauthor of the current paper, and used only for the experiment. In the treat- ment, only instrumental selections (e.g., pi- ano) were employed. The song was arranged to piano solo score and performed by a vir- tual grand piano — the software synthesiser Ivory Grand Pianos standardised by VSTi that emulates “Boseudofer 290 Imperial Grand”.

No other particular artificial instruments were used, except for equipments for auditory cor- rection (i.e., the equaliser, reverb and master- ing effects). The music tempo was fixed as 120 bpm and loop was arranged for continu-

Figure 17: The distribution ofPrisky of the in- dividual Type A problems in Treatment 2. For example, 1 out of 60 Type A problems was ob- served, wherePriskywas less than 0.1.

Figure 18: The distribution ofPsoonerof the in- dividual Type B problems in Treatment 2. For example, 1 out of 40 Type B problems was ob- served, where 0.2<Psooner0.3.

ous experiment. Note that 1 loop is 1 minute and 4 seconds. The sound pressure of the 2 MIX source was normalised as -15 dB and its range is−dB to -0.1 dB (no clip). The for- mat of sound source was 16 bits/44.1 kHz CD quality wave format without any compression.

The average of note tone was D4; the high- est note was F5 and; the lowest note was E1 (as chromatic scale). The density of notes was 250 notes per minute. Average velocity of note was 100 (highest: 127, lowest: 64). The vol- ume of the music was maintained at a con- stant level with the headphones. The volume among each participant was all the same and fixed to proper loudness through the treatment continuously. Results of the questionnaires re- vealed that no participants expressed discom- fort or distaste for the music played during the treatment.

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4.4.2 Results

An overall Prisky was 0.49. The Prisky of indi- vidual participants is available in Appendix 2.

Figure11 presents numbers of risky and safe choices of individual participants in the treat- ment. We can see from the figure the existence of heterogeneity among the participants in be- havioural tendencies in the treatment. For ex- ample,Priskyof some participants (e.g., Partic- ipant 19) was 100 percent; whilePriskyof other participants (e.g., Participant 26) was less than 10 percent. Figure 15 presents the distribu- tion of the individual Prisky in the treatment (SD=0.26). ThePriskyof individual 60 Type A problems is available in Appendix 4. Figure13 presents numbers of risky and safe choices of individual problems in the treatment. Fig- ure17presents the distribution ofPriskyof the individual problems (SD=0.23).

An overallPsoonerwas 0.57. ThePsoonerof in- dividual participants is available in Appendix 3. Figure 12presents numbers of sooner and later choices of individual participants in the treatment. We can see from the figure the exis- tence of heterogeneity among the participants in behavioural tendencies in the treatment. For example, some participants (e.g., Participant 1) chose only sooner options, while others (e.g., Participant 16) chose only later options. Fig- ure 16 presents the distribution of the indi- vidual Psooner in the treatment (SD = 0.34).

The Psooner of individual 40 Type B problems is available in Appendix 5. Figure14presents numbers of sooner and later choices of indi- vidual problems in the treatment. Figure 18 presents the distribution of Psooner of the indi- vidual problems (SD= 0.29). An overall pro- portion of rational choices made among Type C problems was 1.

4.4.3 Questionnaire Analysis

On completion of the treatment, the partici- pants were asked to fill in a questionnaire that contained the same set of questions as Treat- ment 1.

Results of the questionnaire revealed the fol- lowings: First, self-reported familiarity level of the music on a 11-point scale (0=not fa- miliar with; 10=very much familiar with) was extremely low (Min = 0,Max = 6,M = 0.88,SD = 1.46). Second, self-reported at-

tention level on a 11-point scale (0=no atten- tion at all; 10=very much attention) was mod- erate (Min = 0,Max = 10,M = 5.79,SD = 3.03). Third, self-reported music liking on a 11-point scale (0=dislike very much; 10=like very much) was high (Min = 1,Max = 10,M = 7.40,SD = 1.79). Fourth, self-reported in- fluence of the music on decision-making be- haviour on a 11-point scale (0=to no extent;

10=to a very large extent) was low (Min = 0,Max=10,M=2.98,SD=3.09).

4.5 Treatment 3: Noise Treatment

4.5.1 Stimuli

The background sound used in Treatment 3 was “Gaussian white noise”. The format of sound source was 16bits/44.1kHz CD quality wave format without any compression, thus the power of spectrum pattern was evenly at the range from 0 Hz to 22.1 kHz. The sound pressure was normalised as -20 dB, thus the wave form was slightly different from ideal wave form. An amplitude over bit range was cut off. The sound pressure was lower than the other music treatments. This is because the perception of this stimulus was higher than other musical stimulus and we feel more loud- ness under the same sound pressure. To avoid the participants’ uncomfortableness, the level of the sound pressure of this stimulus was de- creased, so that the participants would feel the stimulus was as loud as the stimulus used in the other two treatments. The sound pattern was evenly static across the treatment. No mu- sical pieces were used in the treatment except white noise. The volume among each partic- ipant was all the same and fixed to proper loudness across the treatment. Results of the questionnaires revealed that no participants expressed discomfort or distaste for the noise played during the treatment.

4.5.2 Results

An overallPrisky was 0.54. The Prisky of indi- vidual participants is available in Appendix 2.

Figure19presents numbers of risky and safe choices of individual participants in the treat- ment. We can see from the figure the existence of heterogeneity among the participants in be- havioural tendencies in the treatment. For ex-

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Figure 19: Numbers of risky and safe choices in Treatment 3. For example, Participant 16 was presented with 15 Type A choice problems, and chose risky options in 1 problem and safe op- tions in 14 problems.

Figure 20: Numbers of sooner and later choices of individual participants in Treatment 3. For example, Participant 9 was presented with 15 Type B choice problems, and chose sooner options in 14 problems and later options in 1 problem.

Figure 21: Numbers of risky and safe choices in individual 60 Type A problems in Treatment 3. For example, Problem 1 was performed by 14 participants and 2 of them chose risky options and 12 chose safe options.

Figure 22: Numbers of sooner and later choices in individual 40 Type B problems in Treatment 3. For example, Problem 69 was performed by 17 participants, and 11 of them chose sooner options and 6 chose later options.

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ample, Prisky of some participants (e.g., Par- ticipant 16) was extremely low; while Prisky of other participants (e.g., Participant 7) was high. Figure23presents the distribution of the individual Prisky in the treatment (SD= 0.24).

ThePriskyof individual 60 Type A problems is available in Appendix 4. Figure 21 presents numbers of risky and safe choices of indi- vidual problems in the treatment. Figure 25 presents the distribution of Prisky of the indi- vidual problems (SD=0.22).

Figure 23: The distribution ofPriskyof the indi- vidual participants in Treatment 3. For exam- ple, we observed 3 participants, whosePriskyis such that 0.5<Prisky0.6.

Figure 24: The distribution of Psooner of the individual participants in Treatment 3. For example, we observed 3 participants, whose Priskyis such that 0.1<Prisky0.2.

An overallPsoonerwas 0.65. ThePsoonerof in- dividual participants is available in Appendix 3. Figure 24presents numbers of sooner and later choices of individual participants in the treatment. We can see from the figure the exis- tence of heterogeneity among the participants in behavioural tendencies in the treatment. For example, some participants (e.g., Participant 23) chose only sooner options, while others

Figure 25: The distribution ofPrisky of the in- dividual Type A problems in Treatment 3. For example, 3 out of 60 Type A problems were ob- served, where 0.2<Prisky0.3.

Figure 26: The distribution ofPsoonerof the in- dividual Type B problems in Treatment 3. For example, 1 out of 40 Type B problems was ob- served, where 0.1<Psooner0.2.

(e.g., Participant 3) chose only later options.

Figure 24 presents the distribution of the in- dividualPsooner in the treatment (SD = 0.34).

The Psooner of individual 40 Type B problems is available in Appendix 5. Figure22presents numbers of sooner and later choices of indi- vidual problems in the treatment. Figure 26 presents the distribution ofPsooner of the indi- vidual problems (SD=0.26).

4.5.3 Questionnaire Analysis

On completion of the treatment, the partici- pants were asked to fill in a questionnaire that contained questions: (1) How much attention did you pay to background sound during this treatment? (2) Do you like the sound presented during this treatment? (3) Do you think your decision-making behaviour was influenced by the sound? The questionnaire aimed to clar- ify the participants’ perception of the noise, as

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Figure 27: Numbers of risky and safe choices in Treatment 4. For example, Participant 13 was presented with 21 Type A choice problems, and chose risky options in 5 problem and safe op- tions in 16 problems.

Figure 28: Numbers of sooner and later choices of individual participants in Treatment 4. For ex- ample, Participant 26 was presented with 14 Type B choice problems, and chose sooner options in 10 problems and later options in 4 problems.

Figure 29: Numbers of risky and safe choices in individual 60 Type A problems in Treatment 4.

For example, Problem 19 was performed by 12 participants and 11 of them chose risky options and 1 chose safe options.

Figure 30: Numbers of sooner and later choices in individual 40 Type B problems in Treatment 4. For example, Problem 85 was performed by 19 participants, and 13 of them chose sooner options and 6 chose later options.

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compared to perception of background music in Treatment 1 and 2.

Results of the questionnaire revealed the followings: First, self-reported attention level on a 11-point scale (0=no attention at all;

10=very much attention) was moderate (Min = 0,Max = 10,M = 6.21,SD = 3.77). Sec- ond, self-reported sound liking on a 11-point scale (0=dislike very much; 10=like very much) was extremely low (Min = 0,Max = 8,M = 1.88,SD=2.01). Third, self-reported influence of the sound on decision-making behaviour on a 11-point scale (0=to no extent; 10=to a very large extent) was low (Min = 0,Max = 10,M=2.85,SD=3.18).

4.6 Treatment 4: No Music Treat- ment

4.6.1 Stimuli

No background music/sound was used in Treatment 4. The participants were asked to engage in choice tasks in the presenceneitherof background musicnorof background sound.

4.6.2 Results

An overall Prisky was 0.48. The Prisky of indi- vidual participants is available in Appendix 2.

Figure27 presents numbers of risky and safe choices of individual participants in the treat- ment. We can see from the figure the existence of heterogeneity among the participants in be- havioural tendencies in the treatment. For ex- ample,Priskyof some participants (e.g., Partici- pant 9) was extremely low; whilePriskyof other participants (e.g., Participant 8) was high. Fig- ure 31 presents the distribution of the indi- vidual Prisky in the treatment (SD = 0.21).

ThePriskyof individual 60 Type A problems is available in Appendix 4. Figure 29 presents numbers of risky and safe choices of indi- vidual problems in the treatment. Figure 33 presents the distribution of Prisky of the indi- vidual problems (SD=0.24).

An overallPsoonerwas 0.6. ThePsoonerof indi- vidual participants is available in Appendix 3.

Figure28presents numbers of sooner and later choices of individual participants in the treat- ment. We can see from the figure the existence of heterogeneity among the participants in be- havioural tendencies in the treatment. For ex-

ample, some participants (e.g., Participant 32) chose only sooner options, while others (e.g., Participant 37) chose only later options. Fig- ure 32 presents the distribution of the indi- vidual Psooner in the treatment (SD = 0.34).

The Psooner of individual 40 Type B problems is available in Appendix 5. Figure30presents numbers of sooner and later choices of indi- vidual problems in the treatment. Figure 34 presents the distribution ofPsooner of the indi- vidual problems (SD=0.26).

Figure 31: The distribution ofPriskyof the indi- vidual participants in Treatment 4. For exam- ple, we observed 2 participants, whosePriskyis such that 0.7<Prisky0.8.

Figure 32: The distribution ofPsoonerof the in- dividual participants in Treatment 4. For ex- ample, we observed 1 participant, whosePrisky is such that 0.6<Prisky0.7.

4.6.3 Questionnaire Analysis

No questionnaire was given to the participant in this treatment.

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Figure 33: The distribution of Prisky of the in- dividual Type A problems in Treatment 4. For example, 2 out of 60 Type A problems were ob- served, where 0.6<Prisky0.7.

Figure 34: The distribution ofPsoonerof the in- dividual Type B problems in Treatment 4. For example, 2 out of 40 Type B problems was ob- served, where 0.8<Psooner0.9.

4.7 Payments to Participants

In the experiment, each participant engaged in four treatments, in each of which she/he re- sponded to 30 pairwise choice problems. Thus, she/he responded to a total of 120 choice prob- lems. Among all of 120 choice problems, only one choice problem was determined for which she/he was paid. The determination was made by the following steps:

Step 1: Once each participant completed all decision tasks in the last treatment, computer programmes randomly selected five out of 120 choice problems she/he had responded in the experiment. The selected five choice prob- lems and options she/he had chosen were dis- played on her/his computer screen, as shown in Figure35.

Step 2: She/he was asked to choose one of the five problems. The experimenter announced that she/he could be paid for this one prob-

Consider the bingo cage that contains 50 balls, each numbered from 1 to 50, and only one ball is drawn. An event X is where any ball numbered between 1 and 40 is drawn. An event Y is where any ball numbered between 41 and 50 is drawn.

Sure 3000 yen

Choose between

# 4000 yen with probability 80%

and;

# Sure 3000 yen

4000 yen with probability 80%

Choose between

# Sure 2000 yen today and;

# Sure 2100 yen in one week

Sure 2000 yen today

Choose between

# 400 yen with probability 80%

and;

# Sure 300 yen

400 yen with probability 80%

Choose between

# Sure 1000 yen today and;

# Sure 1050 yen in one week

Sure 1050 yen in one week

Figure 35: An example of five choice problems randomly selected by computer programmes and the participant’s choices. The left column shows selected five choice problems and the right shows options chosen by her/him.

lem.

Step 3: This step was split into the following two different steps (i.e., Step 3-1 and 3-2), de- pending on a type of the choice problem cho- sen by her/him in Step 2 and the option of the problem chosen by her/him during the exper- iment.

Step 3-1: This step applied if the choice prob- lem chosen in Step 2 involved a choice between a risky option (i.e., an option yielding an un- certain payoff) and a safe option (i.e., an option yielding a sure payoff), regardless of whether the choice problem was concerned with choice under risk or intertemporal choice.

If she/he had chosen the safe option, her/his payoff was immediately determined.

Then, she/he was asked to remain seated until payment was ready. For example, if the choice problem chosen in Step 2 was to choose be- tween a risky option that could yield 4000 yen with probability of 80% and a safe option that could yield a sure payoff of 3000 yen (i.e., the choice problems shown in the first and third raws in Figure35), and she/he had chosen the safe option, her/his award amount was im- mediately determined. Then, she/he was in-

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formed that she/he could be given 3000 yen shortly.

On the other hand, if she/he had chosen the risky option, she/he was presented with an empty bingo cage and a set of numbered balls. Then, she/he was asked to put these numbered balls into the empty bingo cage, and draw one ball from the bingo cage. An out- come of the risky option was determined, ac- cording to the ball drawn. The composition of the bingo cage varied, depending on the choice problem and option she/he had chosen. The preparation of the bingo cage and balls was done in view of her/him, staff at KEEL and other participants.

For example, if she/he had chosen the risky option in the abovementioned choice problem, the experimenter prepared the empty bingo cage and balls numbered 1 through 50, and asked her/him to put these 50 balls into the empty bingo cage. Then, she/he was asked to choose and write down any ten numbers from 1 to 50 on a blackboard at the laboratory.

Before asking her/him to draw one ball from the bingo cage, containing 50 balls, the exper- imenter informed her/him that she/he could be given 4000 yen if any of the balls that car- ried numbers you chose and wrote down on the blackboard wasnotdrawn, and no money, otherwise.

Step 3-2: This step applied if the choice prob- lem she/he chose in Step 2 involved an in- centive scheme that payments could be made in the future (e.g., one week after the experi- ment). We employed Japanese practice of us- ing “registered mail for cash” to send her/him a cash payoff, if she/he was to receive deferred payments. Postage costs were borne by the ex- perimenter. For example, if the choice problem was to choose between “a sure payoff of 1000 yen today” and “a sure payoff of 1050 yen in one week”, and her/his choice was the latter, then 1050 yen was received by registered mail one week after the experiment.

5 General Discussion

5.1 Behavioural Tendencies in the Presence of Background Noise

A perusal of previous studies renders to what extent background noise affects the de-

cision makers’ performance. Some (e.g.,Eller- meier and Hellbr ¨uck, 1998; Jones, Miles and Page, 1990; Abikoff, Courtney, Szeibel and Koplewicz,1996;Salam´e and Baddeley,1987) showed that background noise does not af- fect cognitive performance. Others, however, provided an account for noise-induced im- provement (e.g., Usher and Feingold, 2000;

S ¨oderlund and Smart,2007;Baker and Hold- ing,1993;Zentall and Shaw,1980) and noise- induced deterioration in cognitive perfor- mance (e.g.,Schlittmeier and Hellbr ¨uck,2009;

Cassidy and MacDonald,2007;Hygge, Evans and Bullinger,2002;Ylias and Heaven,2003).

The results of the current experiment con- firm that background noise affects perfor- mance in decision making under risk and in- tertemporal decision making.

On the one hand, we observed increased proclivity towards risk-taking behaviour in Type A problems in the presence of back- ground noise, compared to the other back- ground music/sound. Figure 36 shows an overall Prisky in each treatment. We found a significant difference in the participants’ per- formance in the presence of noise (i.e., in Treat- ment 3), compared to silence (i.e., in Treat- ment 4), when they made choice under risk.

An overall Prisky in Treatment 3 and that in Treatment 4 were 0.54 and 0.48, respectively.

The difference between these two proportions was statistically significant (χ2(1) = 5.21,p <

0.05), though there is no statistical difference among hole four treatments (χ2(3) =5.43,p>

0.05).

Figure 36: An overallPriskyin each treatment On the other hand, the current results in- dicate a behavioural tendency that the sooner options were more opted by the participants in Treatment 3 (i.e., in the presence of back-

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Figure 37: An overallPsoonerin each treatment

ground noise), compared to the other three treatments. Figure 37 that shows an overall Psooner in each treatment. A significant dif- ference was observed in the participants’ per- formance in the presence of noise, compared to silence, when they made choice between a sooner option and later option. An overall Psooner was statistically different across all of the four treatments (χ2(3) =19.18,p<0.001).

Much attention is given here to a comparison of an overall Psooner in Treatment 3 and that in Treatment 4: Psooner in the former treatment and the latter were 0.65 and 0.51, respectively.

The difference between these two proportions was statistically significant (χ2(1) =18.66,p<

0.001), though there was no statistical differ- ence between: (1)Psooner in Treatment 1 and 3 (χ2(1) =3.58,p >0.1) and; (2)Psoonerin Treat- ment 1 and 4 (χ2(1) =3.15,p>0.1).

5.2 Observed and Predicted Be- havioural Tendencies

Figure38shows the number of the participants (X-axis) and the level of Prisky (Y-axis) across the four treatment sorted in an ascending or- der. The predicted risky choices refer to the prediction of Prisky of individual participants, assuming that they randomly select options in 60 Type A problems. The observed risky choices refer to the observed Prisky of the indi- vidual participants across the four treatments.

The difference between the predicted and ob- served risky choices (Prisky) is statistically sig- nificant (χ2(1) = 10.71,p < 0.01). If sub- jects randomly select options in 60 problems by fifty-fifty, the prediction of Prisky would be according to binomial distribution. So that, for example the posibility of the (Prisky > 0.9

Figure 38: Predicted and observed each partic- ipant’sPrisky across the four treatments sorted in an ascending order. The solid line corre- sponds to the prediction ofPriskyacross 42 par- ticipants. The dotted line corresponds to the observedPrisky across 42 participants. For ex- ample, from the prediction, we would see only two out of 42 participants, whose Prisky less than 0.4; while we observed 16 participants in the experiment (i.e., across the four treat- ments).

Figure 39: Predicted and observed Prisky of individual Type A problems across the four treatments sorted in an ascending order. The solid line corresponds to the prediction ofPrisky across 60 Type A problems. The dotted line corresponds to the observed Prisky across 60 Type A problems. For example, from the pre- diction, we would see that the risky option should be chosen in 54 out of 60 Type A prob- lems. Yet, we observed in the experiment that the risky option was chosen only in 44 prob- lems.

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Figure 40: Predicted and observed each partic- ipant’sPsooneracross the four treatments sorted in an ascending order. The solid line corre- sponds to the prediction of Psooner across 42 participants. The dotted line corresponds to the observedPsooneracross 42 participants. For example, from the prediction, we would see 38 out of 42 participants, whose Psooner is less than 0.6; while we observed only 17 partici- pants in the experiment (i.e., across the four treatments).

Figure 41: Predicted and observedPsoonerof in- dividual problems across the four treatments sorted in an ascending order. The solid line corresponds to the prediction of Psooner across 40 Type B problems. The dotted line corre- sponds tothe observedPsooneracross 40 Type B problems. For example, from the prediction, we would see that the sooner option should be chosen in 20 out of 40 Type B problems. Yet, we observed in the experiment that the sooner option was chosen only in 13 problems.

would be extreamly lower than observation.

Or even if there are some particular priority or characteristics in the problems, for exam- ple choice between 1 percent to win 1000 and sure as 100 yen, average might be changed but it can not be the reason of this large distribu- tion. We can also see the tendency of the het- erogeneity in each histgrams like as Figure9.

These kind of distribution cannot explain by ordinaly approach which are using statistics.

Figure39shows the number of Type A prob- lems (X-axis) and the level of Prisky (Y-axis) across the four treatment sorted in an ascend- ing order. The predicted risky choices refer to the prediction of Prisky of individual Type A problems, assuming that risky and safe op- tions are selected randomly. The observed risky choices refer to the observed Prisky of the individual problems across the four treat- ments. The difference between predicted and observed risky choices (Prisky) is statistically significant (χ2(1) = 15.50,p < 0.01). Also in this results, if 42 subjects randomly selected the options in each problems by fifty-fifty, the prediction ofPrisky would be according to bi- nomial distribution. So that, for example the posibility of the (Prisky > 0.9 would be ex- treamly lower than observation. In this case, the differencies of the problem characteristics appear to the results. For example, comparison between problem 2 and problem 6. These two kinds of problems has the same pay off amount on the case of win, and only the probability scale is different. Howevere there is signifi- cantly difference of total ration between these results. So in this distribution, there are more complicated mechanism underlying.

Figure40shows the number of the partici- pants (X-axis) and the level of Psooner (Y-axis) across the four treatment sorted in an ascend- ing order. The predicted sooner choices re- fer to the prediction of Psooner of individual participants, assuming that they randomly se- lect options in 40 Type B problems. The ob- served sooner choices refer to the observed Psoonerof the individual participants across the four treatments. The difference between the predicted and observed sooner choices (Psooner) is statistically significant (χ2(1) = 12.25,p <

0.01). If subjects randomly select options in 60 problems by fifty-fifty, the prediction of Priskywould be according to binomial distribu- tion. So that, for example the posibility of the

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(Prisky > 0.9 would be extreamly lower than observation. These results are all about type B problems, so its mechanism would be different from results of type A problem. However in these results, the tendency of the heterogeneity could be observed in wide range. Some partic- ipants selected only later choice and some par- ticipants selected only sooner choice, though there are 0.1 percent to more than 1 percent in- terest per day.

Figure41shows the number of the problems (X-axis) and the level of Psooner (Y-axis) across the four treatment sorted in an ascending or- der. The predicted sooner choices refer to the prediction ofPsoonerof individual Type B prob- lems, assuming that sooner and later options are selected randomly. The observed sooner choices refer to the observed Psooner of indi- vidual Type B problems across the four treat- ments. The difference between predicted and observed sooner choices (Psooner) is statistically significant (χ2(1) = 13.33,p < 0.01). Also in this results, if 42 subjects randomly selected the options in each problems by fifty-fifty, the prediction of Prisky would be according to bi- nomial distribution. So that, for example the posibility of the (Prisky > 0.9 would be ex- treamly lower than observation. In this case, the differencies of the problem characteristics appear to the results. Some problems are very similar pay off in spite of longer delay, and some problems are 1 percent different pay off with only 1 day delay.

6 Concluding Remarks

There have been behavioural outcomes of mu- sic in marketing (e.g.Alpert and Alpert,1988;

Gorn,1982;Milliman, 1982; Park and Young, 1986; Simpkins and Smith,1974) and in psy- chology (e.g. Iwanaga and Ito, 2002; Sund- strom and Sundstrom,1986;Wolf and Weiner, 1972). However no attempts have been made by experimental economists to examine effects of music in economics decision making. With a toolset of experimental economics, this paper has investigated to what extent background music affects the DMs, who engage in decision making under risk and intertemporal decision making. The investigation has been conducted along with the assertion that music can affect human emotion and their behaviour, and is a

way for us to make behaviour either powerful or less powerful.

It should be noted here that this paper has not discussed the effect of “levels” of noise. In the current experiment, level of noise was fixed and set at -20 dB. Different authors, however, used different levels of noise in their experi- ments, involving tasks (e.g., 62 dB and 78 dB inCarlson, Rama, Artchakov and Linnankoski (1997), 90dB inBaker and Holding(1993)). It is of importance to investigate the effects on lev- els of noise presented to the decision makers during choice tasks. On the one hand, low lev- els of noise may improve performance (Alain, Quan, McDonald and Van Roon,2009). Zen- tall and Shaw(1980) showed that high levels of noise (i.e., 69dB) were detrimental though low levels (i.e., 64dB) were not. On the other hand, in their experiment conducted by S ¨oderlund and coauthors (S ¨oderlund and Smart, 2007), they fixed and set level of noise at 80dB and 81dB and their results showed on noise can benefit performance. To claim that level of noise is one of key determinants that affect be- haviour in decision tasks that involve choice under risk and intertemporal choices, one may conduct relevant experiments, varying levels of noise to be presented to the participants.

Findings from the current paper will con- tribute to us to decide what background sound to employ when people engage in decision making. Deciding right background sound in a particular decision task is crucial, as wrong background sound can produce effects that to- tally neglect the objective of the exercise (Mil- liman,1982). Thus, the findings can help man- agers interested in influencing behaviour of employees and consumers. It can also help bankers interested in influencing behaviour of investors, that is, interested in inducing the investors to buy low-risk assets (e.g., govern- ment bonds) and high-risk assets (e.g., mutual funds).

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